# Abstract reasoning: word problems

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## Practice word problems aptitude tests

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## What are word problems?

Word problems are part of numerical reasoning. With word problems you get to see a number of lines with data in it. You must then answer a question. The tricky thing about editorial sums is that you:

• Determine what needs to be calculated.
• Determine which data is relevant.
• Perform the calculation.

The calculation in this case is secondary to the correct interpretation of the information. The disadvantage of assessments is that only the outcome counts. Even if you have reasoned correctly, you may have the answer wrong and you get zero points for that question.

The actual calculations that you must perform are:

subtracting,
• multiplying,
• division,
• fractions,
• percentages,
• decimals,
• estimations.

Although there is an almost infinite number of editorial sums, the following types of sums are usually requested:

• Volume and area.
• Rivers and speed.
• Productivity.
• Filling containers with water.
• Vehicles and speed.
• Profit calculation.

## Examples of word problems

Below you will find some examples with answers and explanations.

## Example 1: volume and surface

The sides of a square increase by 25%. Then, by how much percent does the area of the square increase?

Step 1 – side:

Assume that the side in the old situation is 1. Then in the new situation the side is 1.25.

Step 2 – area:

Surface old = side x side = 1 x 1 = 1
Surface new = side x side = 1.25 x 1.25 = 1.5625

Step 3 – increase:

(New – old) / old x 100 = percentage increase
(1.5625 – 1) / 1 x 100 = 56.25% increase

## Example 2: rivers and speed

A boat sails downstream from A to B and upstream to C (in the middle between A and B) in 19 hours . The river has a current of 4 km/h, the boat sails in standing water at 14 km/h. What is the distance between A and B?

Step 1 – speed downstream:

The boat sails downstream at a speed of 14 + 4 = 18 km per hour.

Step 2 – speed upstream:

The boat travels upstream at a speed of 14 – 4 = 10 km per hour.

Step 3 – distances:

The distance between A and B equals M. Then the distance between B and C equals 0.5 M or M / 2. Because C lies exactly between A and B, so that is half the distance.

Step 3 – calculation:

Then M / 18 is the time the boat does over the distance from A to B. Then (0.5 M) / 10 is also the time that the boat does over the distance from B to C. The total time is 19 hours. So:

19 = M / 18 + 0.5 M / 10
19 = M / 18 + M / 20
M = 180 km

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